BPSC AE cheat sheet

The Constitution of India was adopted on 26 November 1949 and came into force on 26 January 1950; Dr B R Ambedkar chaired the Drafting Committee.

Fundamental Rights occupy Articles 12-35 (Part III); the Right to Constitutional Remedies (Art 32) was called the 'heart and soul' of the Constitution by Ambedkar.

The Directive Principles of State Policy (Part IV, Articles 36-51) are non-justiciable; Article 40 deals with panchayats and Article 44 with a uniform civil code.

The Tropic of Cancer (23.5 degrees N) passes through eight Indian states including Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura and Mizoram.

The monsoon retreats from September; the southwest monsoon supplies about 75 percent of India's annual rainfall, and Mawsynram receives among the world's highest rainfall.

The Reserve Bank of India was nationalised in 1949; monetary policy repo rate changes are decided by the six-member Monetary Policy Committee, created in 2016.

Photosynthesis converts carbon dioxide and water into glucose and oxygen in chloroplasts; the light reaction occurs in thylakoids and the Calvin cycle in the stroma.

The Indian National Congress was founded in 1885 by A O Hume; the Jallianwala Bagh massacre occurred on 13 April 1919 in Amritsar.

Newton's second law F = ma underlies dynamics; the unit of force, the newton, equals 1 kg m/s^2.

Stress = force/area (N/m^2 or Pa); strain is dimensionless; Hooke's law gives stress = E x strain within the elastic limit.

First law of thermodynamics: dQ = dU + dW; for a closed system at constant volume, work is zero and heat supplied equals internal-energy change.

Carnot efficiency of a heat engine is 1 - T_cold/T_hot, with temperatures in kelvin; no real engine exceeds this value.

Ohm's law V = IR; electrical power P = VI = I^2R = V^2/R; resistors in series add, and in parallel their reciprocals add.

Bernoulli's equation for steady incompressible flow: p/rho + v^2/2 + gz = constant along a streamline.

The modulus of elasticity E, shear modulus G and Poisson's ratio nu relate as G = E / (2(1 + nu)) for an isotropic material.

In a four-stroke engine, one thermodynamic cycle takes two crankshaft revolutions; a two-stroke engine completes a cycle in one revolution.

For a simply supported beam with central point load W and span L, maximum bending moment is WL/4 at midspan and maximum shear is W/2 at supports.

For a cantilever with uniformly distributed load w per unit length over length L, maximum BM is wL^2/2 at the fixed end and maximum deflection is wL^4/(8EI).

Working stress method uses permissible stresses with a factor of safety; limit state method applies partial safety factors (1.5 for loads, 1.15 for steel, 1.5 for concrete).

Terzaghi's bearing capacity for a strip footing: q_u = cN_c + gamma D_f N_q + 0.5 gamma B N_gamma, with N factors depending on the friction angle.

Manning's equation for open-channel flow: V = (1/n) R^(2/3) S^(1/2), where R is hydraulic radius and S is bed slope.

The Chezy formula gives V = C sqrt(RS); the hydraulic radius R = A/P, area divided by wetted perimeter.

BOD measures oxygen demanded by microbes to oxidise organic matter over five days at 20 degrees Celsius; COD measures chemical oxidation and is always higher than BOD.

In levelling, the reduced level of a point equals height of instrument minus staff reading; the rise-and-fall method compares consecutive staff readings.

For an ideal gas, pV = mRT; the universal gas constant is 8314 J/(kmol K), and R for air is about 287 J/(kg K).

The Carnot COP of a refrigerator is T_cold/(T_hot - T_cold); for a heat pump it is T_hot/(T_hot - T_cold), temperatures in kelvin.

For a simply supported beam of rectangular section, bending stress sigma = My/I; maximum stress occurs at the extreme fibre, where y = depth/2.

Torsion of a circular shaft: tau/r = T/J = G theta/L; maximum shear stress equals 16T/(pi d^3) for a solid shaft.

Fourier's law of conduction: q = -kA dT/dx; the thermal resistance of a plane wall is L/(kA).

In a four-bar linkage, Grashof's condition states the shortest link plus the longest link is less than or equal to the sum of the other two for continuous relative rotation.

For orthogonal metal cutting, shear angle phi satisfies tan phi = r cos(alpha) / (1 - r sin(alpha)), where r is the chip thickness ratio.

In a vapour-compression refrigeration cycle, the expansion valve is isenthalpic, the compressor is approximately isentropic, and the condenser rejects heat at constant pressure.

In a series RLC circuit at resonance, inductive and capacitive reactances cancel, impedance is purely resistive, and the resonant frequency is 1/(2 pi sqrt(LC)).

Thevenin's theorem replaces any linear two-terminal network by an equivalent voltage source in series with a resistance; Norton's uses a current source in parallel with a resistance.

A transformer's EMF equation is E = 4.44 f N Phi_max; the turns ratio equals the voltage ratio, and current ratio is the inverse.

Synchronous speed of an induction motor is N_s = 120f/P; slip s = (N_s - N_r)/N_s, and rotor frequency equals sf.

For a short transmission line, series impedance alone is modelled; for a long line, ABCD parameters use hyperbolic functions with the propagation constant gamma = sqrt(ZY).

The per-unit system expresses quantities as ratios to base values; base impedance equals (base kV)^2 / base MVA.

A P-controller reduces steady-state error but leaves offset; adding integral action eliminates offset, and derivative action improves transient response and stability.

In a three-phase system, total power P = sqrt(3) V_L I_L cos(phi), where V_L and I_L are line quantities.

Average speed for equal distances at speeds a and b is the harmonic mean 2ab/(a+b), not the arithmetic mean.

Compound interest amount A = P(1 + r/n)^(nt); for continuous compounding A = Pe^(rt).

If a pipe fills a tank in x hours and another empties it in y hours, the net fill rate is 1/x - 1/y per hour.

In a number series, check first differences, then second differences, then ratios; alternating and prime-based patterns are common in aptitude tests.

For a clock, the minute hand gains 5.5 degrees per minute over the hour hand; hands overlap 11 times in 12 hours.

Syllogism conclusions are valid only if true in every possible Venn diagram consistent with the premises; 'some' and 'all' statements need careful diagramming.

For two numbers, product = HCF x LCM; this identity solves many problems involving HCF and LCM.

The sum of the first n natural numbers is n(n+1)/2; the sum of squares is n(n+1)(2n+1)/6.

संधि में दो वर्णों के मेल से उत्पन्न विकार को संधि कहते हैं; स्वर संधि, व्यंजन संधि और विसर्ग संधि इसके तीन भेद हैं।

समास के छह भेद हैं: अव्ययीभाव, तत्पुरुष, कर्मधारय, द्विगु, द्वंद्व और बहुव्रीहि।

संज्ञा के पाँच भेद हैं: व्यक्तिवाचक, जातिवाचक, भाववाचक, समूहवाचक और द्रव्यवाचक।

क्रिया के दो भेद हैं: सकर्मक और अकर्मक; सकर्मक क्रिया का फल कर्म पर पड़ता है।

उपसर्ग शब्द के आरंभ में जुड़कर अर्थ बदलता है, जबकि प्रत्यय शब्द के अंत में जुड़ता है; 'अनु' और 'प्र' उपसर्ग के उदाहरण हैं।

वाक्य के आठ भेद कार्य के आधार पर होते हैं, जिनमें आज्ञार्थक, प्रश्नवाचक, विस्मयादिबोधक और निषेधवाचक प्रमुख हैं।

अलंकार दो प्रकार के होते हैं: शब्दालंकार (अनुप्रास, यमक, श्लेष) और अर्थालंकार (उपमा, रूपक, उत्प्रेक्षा)।

रस के नौ भेद हैं, जिनमें शृंगार, हास्य, करुण, रौद्र, वीर, भयानक, बीभत्स, अद्भुत और शांत रस सम्मिलित हैं।

A gerund is a verb form ending in -ing that functions as a noun, as in 'Swimming is good exercise'; a participle modifies a noun.

Subject-verb agreement: indefinite pronouns such as 'each', 'everyone' and 'neither' take singular verbs; 'either...or' agrees with the nearer subject.

Active to passive: the object becomes the subject and the verb becomes a form of 'be' plus the past participle, keeping the original tense.

Direct to indirect speech: present tenses shift to past, 'today' becomes 'that day', and 'will' becomes 'would' when the reporting verb is past.

Idioms must be learned as units; 'to bite the bullet' means to endure a painful situation bravely, and 'once in a blue moon' means very rarely.

A clause contains a subject and a predicate; a phrase does not. A sentence fragment lacks an independent clause.

Commonly confused pairs: 'affect' is usually a verb and 'effect' a noun; 'principal' means chief, 'principle' means a rule.

In reading comprehension, the main idea is stated in the topic sentence, often first or last in a paragraph; inference questions require conclusions not stated explicitly.

Coding-decoding: identify the shift pattern between letters (for example +2, -1) and apply it consistently to the target word.

Blood relations: draw a family tree with gender and generation levels; vertical lines show parent-child and horizontal lines show siblings or spouses.

Direction sense: track net displacement using coordinates, applying Pythagoras to find the shortest distance from the start.

Seating arrangement: fix the most constrained person first, then place others relative to that anchor; circular arrangements use clockwise/anticlockwise cues.

Data interpretation: compute percentages as (part/whole) x 100 and growth rates as (new - old)/old x 100 before comparing options.

Ratio and proportion: if a:b = c:d then ad = bc; for three quantities, use the LCM method to equalise common terms.

Permutations and combinations: nPr = n!/(n-r)! and nCr = n!/(r!(n-r)!); use combinations when order does not matter.

Probability of an event = favourable outcomes / total outcomes; for independent events, P(A and B) = P(A) x P(B).